Global regularity of solutions for the 3D non-resistive and non-diffusive MHD-Boussinesq system with axisymmetric data

TL;DR

This paper proves that solutions to a 3D MHD-Boussinesq system remain smooth globally under specific axisymmetric conditions with zero swirl, extending previous results and applicable to related convection systems.

Contribution

It establishes global regularity for the 3D non-resistive, non-diffusive MHD-Boussinesq system with axisymmetric initial data and zero swirl components, extending prior work.

Findings

Solutions are globally regular under specified conditions.

Method applicable to magnetic Rayleigh-Bénard convection.

Extends previous regularity results for related systems.

Abstract

In this paper, we will show that solutions of the three-dimensional non-resistive and non-diffusive MHD-Boussinesq system are globally regular if the initial data is axisymmetric and the swirl components of the velocity and the magnetic vorticity are zero. Our main result extends previous ones on the three-dimensional non-resistive MHD system and non-diffusive Boussinesq system, and the method used here can also be applied to the magnetic Rayleigh-B\'{e}nard convection system.